Characterizations of Bounded Singular Integral Operators on the Fock Space and Their Berezin Transforms

Characterizations of Bounded Singular Integral Operators on the Fock Space and Their Berezin Transforms

Year:    2023

Author:    Xingtang Dong, Li Feng

Analysis in Theory and Applications, Vol. 39 (2023), Iss. 2 : pp. 105–119

Abstract

There is a singular integral operators $S_{\varphi}$ on the Fock space $\mathcal{F}^2(\mathbb{C}),$ which originated from the unitarily equivalent version of the Hilbert transform on $L^2(\mathbb{R}).$ In this paper, we give an analytic characterization of functions $\varphi$ with finite zeros such that the integral operator $S_{\varphi}$ is bounded on $\mathcal{F}^2(\mathbb{C})$ using Hadamard’s factorization theorem. As an application, we obtain a complete characterization for such symbol functions $\varphi$ such that the Berezin transform of $S_{\varphi}$ is bounded while the operator $S_{\varphi}$ is not. Also, the corresponding problem in higher dimensions is considered.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.OA-2021-0034

Analysis in Theory and Applications, Vol. 39 (2023), Iss. 2 : pp. 105–119

Published online:    2023-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

Keywords:    Fock space singular integral operators boundedness Berezin transform.

Author Details

Xingtang Dong

Li Feng